Volume Calculator – Volume is the quantification of the three-dimensional space a substance occupies. The SI unit for volume is the cubic meter, or m3. By convention, the volume of a container is typically its capacity, and how much fluid it is able to hold, rather than the amount of space that the actual container displaces.

Volumes of many shapes can be calculated by using well-defined formulas. In some cases, more complicated shapes can be broken down into their simpler aggregate shapes, and the sum of their volumes used to determine total volume. The volumes of other even more complicated shapes can be calculated using integral calculus if a formula exists for the shape’s boundary.

Beyond this, shapes that cannot be described by known equations can be estimated using mathematical methods, such as the finite element method. Alternatively, if the density of a substance is known, and is uniform, the volume can be calculated using its weight. This calculator computes volumes for some of the most common simple shapes.

- Sphere Volume Calculator
- Cone Volume Calculator
- Cube Volume Calculator
- Cylinder Volume Calculator
- Rectangular Tank Volume Calculator
- Capsule Volume Calculator
- Spherical Cap Volume Calculator
- Conical Frustum Volume Calculator
- Ellipsoid Volume Calculator
- Square Pyramid Volume Calculator
- Tube Volume Calculator

Contents

## Sphere Volume Calculator

A sphere is the three-dimensional counterpart of the two-dimensional circle. It is a perfectly round geometrical object that mathematically, is the set of points that are equidistant from a given point at its center, where the distance between the center and any point on the sphere is the radius **r**.

Likely the most commonly known spherical object is a perfectly round ball. Within mathematics, there is a distinction between a ball and a sphere, where a ball comprises the space bounded by a sphere.

Regardless of this distinction, a ball and a sphere share the same radius, center, and diameter, and the calculation of their volumes is the same. As with a circle, the longest line segment that connects two points of a sphere through its center is called the diameter, **d**. The equation for calculating the volume of a sphere is provided below:

Example :

Elsa wants to fill a perfectly spherical water balloon with radius 0.15 ft with vinegar to use in the water balloon fight against her arch-nemesis Hilda this coming weekend. The volume of vinegar necessary can be calculated using the equation provided below:

volume = 4/3 × π × 0.15^{3} = 0.141 ft^{3}

### Free Online Sphere Volume Calculator

## Cone Volume Calculator

A cone is a three-dimensional shape that tapers smoothly from its typically circular base to a common point called the apex (or vertex). Mathematically, a cone is formed similarly to a circle, by a set of line segments connected to a common center point, except that the center point is not included in the plane that contains the circle (or some other base). Only the case of a finite right circular cone is considered on this page. Cones comprised of half-lines, non-circular bases, etc. that extend infinitely will not be addressed. The equation for calculating the volume of a cone is as follows:

**Example**: Paige is determined to walk out of the ice cream store with her hard earned $5 well spent. While she has a preference for regular sugar cones, the waffle cones are indisputably larger. She determines that she has a 15% preference for regular sugar cones over waffle cones and needs to determine whether the potential volume of the waffle cone is ≥ 15% more than that of the sugar cone. The volume of the waffle cone with a circular base with radius 1.5 in and height 5 in can be computed using the equation below:

volume = 1/3 × π × 1.5^{2} × 5 = 11.781 in^{3}

Paige also calculates the volume of the sugar cone and finds that the difference is < 15%, and decides to purchase a sugar cone. Now all she has to do is use her angelic, childlike appeal to manipulate the staff into emptying the containers of ice cream into her cone.

### Free Online Cone Volume Calculator

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## Cube Volume Calculator

A cube is the three-dimensional analog of a square, and is an object bounded by six square faces, three of which meet at each of its vertices, and all of which are perpendicular to their respective adjacent faces. The cube is a special case of many classifications of shapes in geometry including being a square parallele piped, an equilateral cuboid, and a right rhombohedron. Below is the equation for calculating the volume of a cube:

volume = a^{3}

where **a** is edge length of the cube

EX: Sam, who was born in Wyoming (and has never left the state), recently visited his ancestral homeland of Nebraska. Overwhelmed by the magnificence of Nebraska and the environment unlike any other he had previously experienced, Sam knew that he had to bring some of Nebraska home with him. Sam has a cubic suitcase with edge lengths of 2 feet, and calculates the volume of soil that he can carry home with him as follows:

volume = 2^{3} = 8 ft^{3}